I was thinking about how the IVs of wild Pokemon are created. If they're created completely at random, that means that there is a 1/32 chance for an IV to be 31. This means that the probability of an IV not being 31 is 31/32.

Continuing the argument further, the probability that a Pokemon in the wild has all its 6 IVs not 31 is (31/32)^6 = 0.82655.

This means that the probability that a wild Pokemon has at least one of its IVs a perfect 31 is 1 - 0.82655 = 0.17345, or 17.345%. This is roughly 1 in 6 wild Pokemon (slightly more than that, in fact).

I'd like to know if this translates to what really happens, since I'm thinking that "1 in 6" Pokemon is too high of a percentage. My hunch is, if there are indeed 1 in 6 Pokemon to have a perfect IV in at least one of the stats, then the IVs are truly generated at random when a wild Pokemon appears. If not, then the IVs for wild Pokemon are not generated completely randomly, but there is a bias towards low or high IVs.

Is there anyone having somehow already tested this can shed some light on the matter? Feedback would be appreciated even if you had done this in Advance, GSC or even RBY, instead of DP.